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Question

In the given figure, $$XY \parallel BC$$. Find the length of XY, given BC = 6 cm
1817382_3f5c7fe8d57c44c99d1e0e7c867bc56b.jpg


Solution

Given: XY || BC


To find: XY


Since, XY || BC, AB is transversal, then, 

$$\Delta AXY = \Delta ABC$$ [by corresponding angles] Since, XY || BC, AC is transversal, then, 

$$\Delta AYX = \Delta ABC$$ [by corresponding angles] In $$\Delta AXY$$ and $$\Delta$$ABC


$$\angle AXY = \angle ABC$$


$$\angle AYX = \angle ACB$$


$$\Delta $$ AXY a $$\Delta$$ ABC [by AA similarity] Since, triangles are similar, hence corresponding sides will be proportional.

$$\therefore \frac {AX}{AB} = \frac {XY}{BC} = \frac {AY}{AC}$$ 

$$XY = \frac{6}{4}$$

XY = 1.5cm


Mathematics

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